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Map showing the extent of Mesopotamia. Shown are Washukanni, Nineveh, Hatra, Assur, Nuzi, Palmyra, Mari, Sippar, Babylon, Kish, Nippur, Isin, Lagash, Uruk, Charax Spasinu and Ur, from north to south.

Mesopotamia is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the Fertile Crescent, in modern days roughly corresponding to most of Iraq, Kuwait, the eastern parts of Syria, Southeastern Turkey, and regions along the Turkish–Syrian and Iran–Iraq borders.

The Sumerians and Akkadians (including Assyrians and Babylonians) dominated Mesopotamia from the beginning of written history (c. 3100 BC) to the fall of Babylon in 539 BC, when it was conquered by the Achaemenid Empire. It fell to Alexander the Great in 332 BC, and after his death, it became part of the Greek Seleucid Empire.

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Babylonian approximation to the square root of 2
Babylonian mathematics refers to the mathematics developed by the ancient Mesopotamians. The earliest writing developed by the Sumerians (ca. 3500 BC) was in fact not words, but numbers — accounting records and tokens. From ca. 3000 BC they developed a complex system of metrology, a move from purely concrete accounting to abstract mathematics. From 2600 BC onwards, we find multiplication tables on clay tablets, geometrical exercises, and division problems. The sexagesimal (base-60) numeral system also comes from this period. This is the source of our modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60×6) degrees in a circle.

During the First Babylonian Dynasty (ca. 1700 – 1531 BC (short chronology)), Babylonian mathematicians were able to make great advances for two reasons — firstly, the number 60 is a highly composite number, facilitating calculations with fractions, and second, unlike the Egyptians and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values (much as in our modern base-ten system). They worked with fractions, algebra, quadratic and cubic equations, the Pythagorean theorem, Pythagorean triples, and possibly trigonometric functions.

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...... that by the 13th century, the Tayy were the dominant Arab tribe in the Syrian steppe, Upper Mesopotamia and north-central Arabia?
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King Melishipak presents his daughter to the goddess Nannaya
...Babylonian astronomy refers to the astronomical theories and methods that were developed in ancient Mesopotamia. Babylonian astronomy formed the basis for much of the later astronomical traditions that developed in Greece, India, the Middle East and ultimately of modern Western astronomy.

Astral theology, which gave planetary gods an important role in Mesopotamian mythology and religion, began with the Sumerians (before 2000 BC), and created a place of importance for the study of astronomical phenomena. Texts from the First Babylonian Dynasty (ca. 1700 – 1531 BC (short chronology)), show the earliest use of mathematics to describe the variation in day length over a year, and the Venus tablet of Ammisaduqa is the earliest evidence that planetary phenomena were recognized as periodic.

During the 8th and 7th centuries BC, Babylonian astronomers developed a new empirical approach to astronomy. They began studying philosophy dealing with the ideal nature of the universe and began employing an internal logic within their predictive planetary systems. This was an important contribution to astronomy and the philosophy of science, and some scholars have referred to this new approach as the first scientific revolution.

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